Heisenberg Uncertainty Relation (Indeterminacy Relations)

  • Paul Busch
  • Brigitte Falkenburg
The term Heisenberg uncertainty relation is a name for not one but three distinct trade-off relations which are all formulated in a more or less intuitive and vague way in Heisenberg's seminal paper of 1927 [1]. These relations are expressions and quantifications of three fundamental limitations of the operational possibilities of preparing and measuring quantum mechanical systems which are stated here informally with reference to position and momentum as a paradigmatic example of canonically conjugate pairs of quantities:
  1. (A)

    It is impossible to prepare states in which position and momentum are simultaneously arbitrarily well localized. In every state, the probability distributions of these ► observables have widths that obey an uncertainty relation.

  2. (B)

    It is impossible to make joint measurements of position and momentum. But it is possible to make approximate joint measurements of these observables, with inaccuracies that obey an uncertainty relation.

  3. (C)

    It is impossible to measure position without disturbing momentum, and vice versa. The inaccuracy of the position measurement and the disturbance of the momentum distribution obey an uncertainty relation.



Uncertainty Relation Uncertainty Principle Physical Review Letter Quantum Mechanical System Atom Interferometer 
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Primary Literature

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Secondary Literature

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    Jammer, M.: The Philosophy of Quantum Mechanics (Wiley, New York, 1974).Google Scholar
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    Busch, P., T. Heinonen, P.J. Lahti: Heisenberg’s uncertainty principle. arXiv:quant-ph/0609185.Google Scholar
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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Paul Busch
  • Brigitte Falkenburg

There are no affiliations available

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